I have being looking for a way to differentiate between someone who is sexually attracted to children but has not acted on the urge and a pedophile who has actually acted on their urges.
Pedophile is sexual attracted to children.
Pederast is a man who indulges in sex with boys.
Is it sexual predator? or does it change to being a pedophile rapist? Since children are unable to consent it would be rape.
It's come up lately in a lot of videos I watch where they have shown pedophiles coming forward and talking about their lives. Many of these seem to have the urges but have not crossed the line of sex or interacting with children. However we call both types pedophiles.
Best Answer
There is no single word that I know of. I think RaceYouAnytime's suggestion of "child molester" fits well.
Other appropriate phrases for someone who has sex with children are "child abuser", "sexual abuser", "perpetrator of child sexual abuse". The three-word phrase "child sexual abuser" is formally ambiguous about which party is the child, so it may not be the best choice.
The use of "pedophile" that you mention is not really appropriate for a formal context due to the vagueness that you mention. The words p(a)edophile/p(a)edophilia have a specific definition in psychology that is not equivalent to "child molester/child molestation". As Wikipedia indicates, in psychology "pedophilia" is defined as sexual attraction (often exclusively) to prepubescent children. Child sexual abuse on the other hand covers sexual activity with children regardless of how the perpetrator felt about it; and in a legal sense, it encompasses abuse of adolescents who are still below the age of consent in their jurisdiction.